Roman Ingarden’s Objectivity vs. Subjectivity as a problem of Translatability

Ingarden (1962, 1964) postulates that artworks exist in an “Objective purely intentional” way. According to this view, objectivity and subjectivity are opposed forms of existence, parallel to the opposition between realism and idealism. Using arguments of cognitive science, experimental psychology, and semiotics, this lecture proposes that, particularly in the aesthetic phenomena, realism and idealism are not pure oppositions; rather they are aspects of a single process of cognition in different strata. Furthermore, the concept of realism can be conceived as an empirical extreme of idealism, and the concept of idealism can be conceived as a pre-operative extreme of realism. Both kind of systems of knowledge are mutually associated by a synecdoche, performing major tasks of mental order and categorisation. This contribution suggests that the supposed opposition between objectivity and subjectivity, raises, first of all, a problem of translatability, more than a problem of existential categories. Synecdoche seems to be a very basic transaction of the mind, establishing ontologies (in the more Ingardean way of the term). Wegrzecki (1994, 220) defines ontology as “the central domain of philosophy to which other its parts directly or indirectly refer”. Thus, ontology operates within philosophy as the synecdoche does within language, pointing the sense of the general into the particular and/or viceversa. The many affinities and similarities between different sign systems, like those found across the interrelationships of the arts, are embedded into a transversal, synecdochic intersemiosis. An important question, from this view, is whether Ingardean’s pure objectivities lie basically on the impossibility of translation, therefore being absolute self-referential constructions. In such a case, it would be impossible to translate pure intentionality into something else, like acts or products.

Constructions and situations : a constructivist reading of Hegel's System

The object of this work is Hegel's Logic, which comprises the first third of his philosophical System that also includes the Philosophy of Nature and the Philosophy of Spirit. The work is divided into two parts, where the first part investigates Hegel s Logic in itself or without an explicit reference to rest of Hegel's System. It is argued in the first part that Hegel's Logic contains a methodology for constructing examples of basic ontological categories. The starting point on which this construction is based is a structure Hegel calls Nothing, which I argue to be identical with an empty situation, that is, a situation with no objects in it. Examples of further categories are constructed, firstly, by making previous structures objects of new situations. This rule makes it possible for Hegel to introduce examples of ontological structures that contain objects as constituents. Secondly, Hegel takes also the very constructions he uses as constituents of further structures: thus, he is able to exemplify ontological categories involving causal relations. The final result of Hegel's Logic should then be a model of Hegel s Logic itself, or at least of its basic methods. The second part of the work focuses on the relation of Hegel's Logic to the other parts of Hegel's System. My interpretation tries to avoid, firstly, the extreme of taking Hegel's System as a grand metaphysical attempt to deduce what exists through abstract thinking, and secondly, the extreme of seeing Hegel's System as mere diluted Kantianism or a second-order investigation of theories concerning objects instead of actual objects. I suggest a third manner of reading Hegel's System, based on extending the constructivism of Hegel's Logic to the whole of his philosophical System. According to this interpretation, transitions between parts of Hegel's System should not be understood as proofs of any sort, but as constructions of one structure or its model from another structure. Hence, these transitions involve at least, and especially within the Philosophy of Nature, modelling of one type of object or phenomenon through characteristics of an object or phenomenon of another type, and in the best case, and especially within the Philosophy of Spirit, transformations of an object or phenomenon of one type into an object or phenomenon of another type. Thus, the transitions and descriptions within Hegel's System concern actual objects and not mere theories, but they still involve no fallacious deductions.

Planar subgraphs without low-degree nodes

We study the following problem: given a geometric graph G and an integer k, determine if G has a planar spanning subgraph (with the original embedding and straight-line edges) such that all nodes have degree at least k. If G is a unit disk graph, the problem is trivial to solve for k = 1. We show that even the slightest deviation from the trivial case (e.g., quasi unit disk graphs or k = 1) leads to NP-hard problems.